An electric dipole has a fixed dipole moment `vecp`, which makes angle `theta` with respect to x-aixs. When subjected to an electric field `vec(E)_(1)=Ehati`, it experiences a torque `vec(T)_(1)=tauhatk`. When subjected to another electric field `vec(E)_(2)=sqrt3Ehatj` it experiences a torque `vec(T)_(2)=-vec(T)_(1)`. The angle `theta` is

Options

A. `60^(@)`
B. `90^(@)`
C. `30^(@)`
D. `45^(@)`

Answer

A

Explanation

` T = PE sin theta ` Torque experienced by the dipole in an
electric field , `vec(T) = vec(P) cc vec(E)`
`vec(p) = p cos hat(i) + p sin theta hat(j) rArr vec(E)_(1) = E vec(i)`
`vec(T)_(1) = vec(p) xx vec(E) _(1) = (rho cos theta hat(i) + p sin theta hat(j)) cc E (hat(i))`
`tau hat(k) = p E sin theta (- hat(k))` (i)
`vec(E)_(2) = sqrt(3) E_(1) hat(j)`
`vec(T) _(2) = p cos theta hat(i) + p sin theta hat(j) xx sqrt(3) E_(1) hat(j)`
`tau hat(k) = sqrt(3) p E_(1) cos theta hat(k)` (ii)
From eqns. (i) and (ii)
`p E sin theta = sqrt(3) p E cos rArr tan theta = sqrt(3) :. theta = 60^(@)`